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Secular dynamics in extrasolar systems with two planets in mutually inclined orbits

Published online by Cambridge University Press:  30 May 2022

Rita Mastroianni Open the ORCID record for Rita Mastroianni [Opens in a new window]  and
Christos Efthymiopoulos
Rita Mastroianni
Affiliation:
Dep. of Mathematics Tullio Levi-Civita, University of Padua via Trieste 63, 35121 Padova, Italy email: rita.mastroianni@math.unipd.it
Christos Efthymiopoulos
Affiliation:
Dep. of Mathematics Tullio Levi-Civita, University of Padua via Trieste 63, 35121 Padova, Italy email: cefthym@math.unipd.it
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Abstract

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We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.

Keywords

Celestial mechanicsPlanetary systems
Type
Research Article
Information
Proceedings of the International Astronomical Union , Volume 15 , Symposium S364: Multi-scale (Time and Mass) Dynamics of Space Objects (Oct 2021) , October 2019 , pp. 191 - 196
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of International Astronomical Union

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